Advertisement

Existential instantiation and strong normalization

  • G. Mints
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1234)

Abstract

We present a new manageable formulation of natural deduction with a rule of existential instantiation ∃xA[x]/A[b]. It simplifies skolemizing devices of earlier formulations, includes a new rule for disjunction and admits a proof of strong normalization. This opens way to the treatment of new systems for which only normal form theorems are known.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gentzen G.: Untersuchungen über das logische Schliessen. Mathematische Zeitschrift, 39 (1934) 176–210, 405–431Google Scholar
  2. 2.
    Girard J.-Y., Lafont Y., Taylor P.: Proofs and Types, Cambridge University Press, Cambridge (1988)Google Scholar
  3. 3.
    Leivant D.: Existential instantiation in a system of natural deduction, Mathematish Centrum-ZW 13–73 (1973)Google Scholar
  4. 4.
    Mints G.: Lewis Systems and the System T. In Mints G.: Selected Papers in Proof Theory, North-Holland-Bibliopolis (1993), 221–294 (Russian Original 1974)Google Scholar
  5. 5.
    Mints G.: A Normal Form Theorem for Second-order Classical Logic with an Axiom of Choice, Math. USSR Izvestiya 32 N3 (1989) 587–605Google Scholar
  6. 6.
    Mints G.: Normal Deduction in the Intuitionistic Linear Logic, CSLI report, (1996)Google Scholar
  7. 7.
    Prawitz D.: Natural Deduction, Almquist and Wiksell (1965)Google Scholar
  8. 8.
    Prawitz D.: Ideas and Results in Proof Theory, In Proc. 2-nd Scand.Logic Symp., North-Holland, (1972) 235–308Google Scholar
  9. 9.
    Quine W.V.: On natural deduction, Journal of Symbolic Logic 15 (1950) 93–102Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • G. Mints
    • 1
  1. 1.Dept. of PhilosophyStanford UniversityStanfordUSA

Personalised recommendations